Summary: An Improved Lower Bound for the Time Complexity
of Mutual Exclusion
James H. Anderson and Yong-Jik Kim
Department of Computer Science
University of North Carolina at Chapel Hill
January 2002, Revised September 2002
Abstract
We establish a lower bound
of
23 N= log log N) remote memory references for N-process mutual
exclusion algorithms based on reads, writes, or comparison primitives such as test-and-set and compare-
and-swap. Our bound improves an earlier lower bound
of
34 log N= log log log N) established by
Cypher. Our lower bound is of importance for two reasons. First, it almost matches the (log N) time
complexity of the best known algorithms based on reads, writes, or comparison primitives. Second,
our lower bound suggests that it is likely that, from an asymptotic standpoint, comparison primitives
are no better than reads and writes when implementing local-spin mutual exclusion algorithms. Thus,
comparison primitives may not be the best choice to provide in hardware if one is interested in scalable
synchronization.